9.2 Direct Numerical Simulation (DNS)
275
9.2.1 Example: Spatial Decay of Grid Turbulence
As an illustrative example of what can be accomplished with DNS, we shall
take a deceptively simple flow, the flow created by an oscillating grid in a
large body of quiescent fluid. The oscillation of the grid creates turbulence
which decreases in intensity with distance from the grid. This process of
energy transfer away from the oscillating grid is usually called turbulent dzffusion; energy transfer by turbulence plays an important role in many flows
so its prediction is important but it is surprisingly difficult to model. Briggs
et al. (1996) made simulations of this flow and obtained good agreement with
the experimentally determined rate of decay of the turbulence with distance
from the grid. The energy decays approximately as x - ~ with 2 < a < 3;
determination of the exponent a is difficult both experimentally and computationally because the rapid decay does not provide a large enough region to
allow one to compute its value accurately.
Distme from
t k source
I
Fig. 9.1. Contours of the kinetic energy on a plane in the flow created by an
oscillating grid in a quiescent fluid; the grid is located at the top of the figure.
Energetic packets of fluid transfer energy away from the grid region. F'rorn Briggs
et al. (1996)
Using visualizations based on simulations of this flow, Briggs et al. (1996)
showed that the dominant mechanism of turbulent diffusion in this flow is
the movement of energetic parcels of fluid through the undisturbed fluid.
This may seem a simple and logical explanation but is contrary to earlier
proposals. Figure 9.1 shows the contours of the kinetic energy on one plane
in this flow. One sees that the large energetic regions are of approximately
the same size throughout the flow but there are fewer of them far from the
grid. The reasons are that those parcels that propagate parallel to the grid do
not move very far in the direction normal to the grid and that small 'blobs'
of energetic fluid are quickly destroyed by the action of viscous diffusion.
The results were used to test turbulence models. A typical example of
such a test is shown in Fig. 9.2 in which the profile to the flux of turbulent
kinetic energy is given and compared with the predictions of some commonly
used turbulence models. It is clear that the models do not work very well even
in a flow as simple as this one. The probable reason is that the models were
275
9.2.1 Example: Spatial Decay of Grid Turbulence
As an illustrative example of what can be accomplished with DNS, we shall
take a deceptively simple flow, the flow created by an oscillating grid in a
large body of quiescent fluid. The oscillation of the grid creates turbulence
which decreases in intensity with distance from the grid. This process of
energy transfer away from the oscillating grid is usually called turbulent dzffusion; energy transfer by turbulence plays an important role in many flows
so its prediction is important but it is surprisingly difficult to model. Briggs
et al. (1996) made simulations of this flow and obtained good agreement with
the experimentally determined rate of decay of the turbulence with distance
from the grid. The energy decays approximately as x - ~ with 2 < a < 3;
determination of the exponent a is difficult both experimentally and computationally because the rapid decay does not provide a large enough region to
allow one to compute its value accurately.
Distme from
t k source
I
Fig. 9.1. Contours of the kinetic energy on a plane in the flow created by an
oscillating grid in a quiescent fluid; the grid is located at the top of the figure.
Energetic packets of fluid transfer energy away from the grid region. F'rorn Briggs
et al. (1996)
Using visualizations based on simulations of this flow, Briggs et al. (1996)
showed that the dominant mechanism of turbulent diffusion in this flow is
the movement of energetic parcels of fluid through the undisturbed fluid.
This may seem a simple and logical explanation but is contrary to earlier
proposals. Figure 9.1 shows the contours of the kinetic energy on one plane
in this flow. One sees that the large energetic regions are of approximately
the same size throughout the flow but there are fewer of them far from the
grid. The reasons are that those parcels that propagate parallel to the grid do
not move very far in the direction normal to the grid and that small 'blobs'
of energetic fluid are quickly destroyed by the action of viscous diffusion.
The results were used to test turbulence models. A typical example of
such a test is shown in Fig. 9.2 in which the profile to the flux of turbulent
kinetic energy is given and compared with the predictions of some commonly
used turbulence models. It is clear that the models do not work very well even
in a flow as simple as this one. The probable reason is that the models were